A Re-Evaluation of the Run Rules Control Charts for Monitoring the Coefficient of Variation

Khai Wah Khaw,Xinying Chew

doi:10.19139/soic-2310-5070-717

Abstract

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean should be monitored. Castagliola et al. (2013a) proposed the two-sided run rules (RR) control charts for monitoring the CV and it is found that the RR CV charts revealed the problem of ARL-biased performances, especially when the monitored sample size is small, for detecting downward CV shifts. This paper alters the RR CV chart by suggesting the two one-sided run rules (ORR) CV charts achieve the unbiased ARL performances. Additionally, this paper also investigates the ORR CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in Castagliola et al. (2013a). A Markov chain model is established for designing the proposed charts. The statistical performances of the ORR CV, RR CV and Shewhart CV (SH CV) charts are compared in terms of the average run length (ARL) and EARL criteria. The results show that the proposed charts surpass the RR CV and SH CV charts for detecting small and moderate upward and downward CV shifts. The implementation of the ORR CV charts is illustrated with an example using a real dataset.

Highlights

Statistical Process Control (SPC) is a powerful collection of problem-solving tools that can be used to control and improve the quality of a process through the reduction of variability
It is natural to explore the use of the coefficient of variation (CV), which monitors the ratio of the standard deviation to the mean, in process monitoring
This paper investigates the one-sided run rules (ORR) CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in [21]

Summary

Introduction

Statistical Process Control (SPC) is a powerful collection of problem-solving tools that can be used to control and improve the quality of a process through the reduction of variability. In some of the real-life scenarios, a quality practitioner prefers to use an intermediate type control chart to monitor the production process due to its simplicity To fill this gap in research, Castagliola et al [21] proposed the intermediate control charts to monitor the CV, i.e. the two-sided run rules CV (RR CV) charts. The two-sided RR CV charts revealed the problem of ARL-biased performances, especially when the monitored sample size is small, for detecting downward CV shifts [21]. In most of the industrial scenarios, practitioners do not have knowledge of the exact CV shift size To tackle this issue, this paper investigates the ORR CV charts in terms of the expected average run length (EARL) criterion, which is not discussed in [21]. A summary of the findings and suggestions for future research are provided

Basic Properties of Sample CV

The ORR CV Charts

Numerical Comparison

An Illustrated Example

Conclusion